A novel approach to calculating the kinetically derived maximum dose

Abstract

The kinetically derived maximal dose (KMD) provides a toxicologically relevant upper range for the determination of chemical safety. Here, we describe a new way of calculating the KMD that is based on sound Bayesian, theoretical, biochemical, and toxicokinetic principles, that avoids the problems of relying upon the area under the curve (AUC) approach that has often been used. Our new, mathematically rigorous approach is based on converting toxicokinetic data to the overall, or system-wide, Michaelis–Menten curve (which is the slope function for the toxicokinetic data) using Bayesian methods and using the “kneedle” algorithm to find the “knee” or “elbow”—the point at which there is diminishing returns in the velocity of the Michaelis–Menten curve (or acceleration of the toxicokinetic curve). Our work fundamentally reshapes the KMD methodology, placing it within the well-established Michaelis–Menten theoretical framework by defining the KMD as the point where the kinetic rate approximates the Michaelis–Menten asymptote at higher concentrations. By putting the KMD within the Michaelis–Menten framework, we leverage existing biochemical and pharmacological concepts such as “saturation” to establish the region where the KMD is likely to exist. The advantage of defining KMD as a region, rather than as an inflection point along the curve, is that a region reflects uncertainty and clarifies that there is no single point where the curve is expected to “break;” rather, there is a region where the curve begins to taper off as it approaches the asymptote (Vmax in the Michaelis–Menten equation).